Method of assaying compressive strength of rock

Abstract

A method of assaying the compressive strength of rock comprises testing a primary plurality of rock samples of similar lithology, at least some of which have different porosities, to determine, for each sample respectively, a value corresponding to compressive strength and a value corresponding to porosity. A first series of pairs of electrical compressive strength and porosity signals, the signals of each pair corresponding, respectively, to the compressive strength and porosity values for a respective one of the samples, is generated. These signals are processed by a computer to extrapolate additional such pairs of signals and generate a second series of electrical signals corresponding to compressive strength as a function of porosity. The second series of signals may correspond to unconfined compressive strength, and may be further processed, to generate a cumulative series of signals, using electrical adjustment signals corresponding to other conditions affecting the compressive strength of the rock. Site characteristics of the rock for a wellbore locus, at a plurality of sites along the length of the locus, and as the rock would be addressed by a drill bit, are determined. At least one of these site characteristics is porosity. The site characteristics are used to generate a plurality of site signals, which, upon processing with the second series of signals (or cumulative series, if any), generate in-situ compressive strength signals corresponding to the in-situ compressive strengths of the rock at the respective sites.

Claims

1. A method of assaying the compressive strength of rock comprising the steps of:

testing a primary plurality of rock samples of similar lithology, at least some of which have different porosities, to determine, for each sample respectively, a compressive strength and a porosity;

generating a first series of pairs of electrical compressive strength and porosity signals, the signals of each pair corresponding, respectively, to the compressive strength and porosity for a respective one of said samples; and

processing the compressive strength and porosity signals to extrapolate additional such pairs of signals and generate a second series of electrical signals corresponding to compressive strength as a function of porosity.

2. The method of claim 1 wherein said processing includes bounding said second series by an electrical maximum porosity signal corresponding to a maximum value for porosity.

3. The method of claim 2 comprising iteratively processing electrical signals potentially corresponding to: said maximum value for porosity and a paired value for a minimum unconfined compressive strength, a value for a maximum unconfined compressive strength, and a mineralogical value for the lithology, to generate multiple potential second series;

and using as said second series the potential second series corresponding to a function whose graphical representation is a logarithmic decline most nearly fitting the upper periphery of a cloud of data points corresponding to said first series of signals on a Cartesian graph of compressive strength versus porosity.

4. The method of claim 3 wherein the compressive strength so determined for each of said samples is an unconfined compressive strength.

5. The method of claim 4 comprising so processing to generate said second series such that said second series corresponds to a function of the form:

S.sub.e =(1-.phi./.phi..sub.max).sup..alpha.

=effective solidity

.sigma..sub.u =said unconfined compressive strength

.sigma..sub.umax =said maximum unconfined compressive strength

.sigma..sub.umin =said minimum unconfined compressive strength

.phi.=porosity

.phi..sub.max =said maximum porosity

.alpha.=said mineralogy value.

6. The method of claim 3 comprising generating a plurality of electrical adjustment signals corresponding to values of at least one other condition affecting the compressive strength of lithologically similar rock; and

processing said adjustment signals to generate a cumulative series of electrical signals corresponding to adjusted compressive strength as a function of porosity and said other condition.

7. The method of claim 6 comprising generating at least some of said adjustment signals as stress adjustment signals corresponding to functions of changes in rock strength due to confinement stress.

8. The method of claim 7 wherein the generation of said stress adjustment signals includes testing a secondary plurality of rock samples of similar lithology to the primary samples, and at least some of which have different porosities, under laterally confined conditions, to determine for each of said other samples, respectively, a confined compressive strength and a porosity;

generating a third series of pairs of electrical confined compressive strength and porosity signals, the signals of each such pair corresponding, respectively, to the confined compressive strength and porosity for a respective one of said secondary samples;

processing the confined compressive strength and porosity signals of said third series to extrapolate additional such pairs of signals and generate a fourth series of electrical signals corresponding to confined compressive strength as a function of porosity.

9. The method of claim 8 wherein said processing of said third series includes bounding said fourth series by an electrical maximum porosity signal corresponding to a maximum value for porosity.

10. The method of claim 9 further comprising so generating a plurality of alternative such fourth series, each of said alternative fourth series from respective samples so tested at a respective lateral confining force;

using the signals of said plurality of alternative fourth series to determine a principal stress relationship value;

generating an electrical signal corresponding to said principle stress relationship value;

and processing said signal corresponding to the principle stress relationship value to generate said cumulative series of signals.

11. The method of claim 7 comprising generating others of said adjustment signals as orientation adjustment signals corresponding to changes in compressive strength due to dip angle of a bedding plane of the rock.

12. The method of claim 11 comprising testing at least two sub-sets of a tertiary plurality of rock samples of similar lithology, the samples of each sub-set having different dip angles with respect to horizontal but the same porosity, to determine, for each of said tertiary samples, a set of orientation variables; the generation of said orientation adjustment signals including first generating a plurality of electrical orientation variable signals corresponding, respectively, to said orientation variables, the orientation variables occurring in pairs, one pair for each sample, and the orientation variables of each pair corresponding, respectively, to relative dip angle and compressive strength.

13. The method of claim 12 wherein the porosities of said two subsets of tertiary rock samples differ.

14. The method of claim 13 comprising processing said orientation variable signals to generate signals corresponding to the orientation variables at maximum porosity and minimum porosity for said lithology.

15. The method of claim 14 comprising processing said orientation variable signals to generate intermediate orientation signals to correspond, respectively, to:

.theta.=dip angle relative to a prospective borehole axis

f.sub.1 =a maximum percent reduction in compressive strength, at.theta..sub.c and zero porosity, due to dip angle,

f.sub.2 =a maximum percent reduction in compressive strength at.theta..sub.c and maximum porosity, due to dip angle,

f.sub.3 =a maximum percent increase in compressive strength at.theta.=90.degree. and zero porosity, due to dip angle,

f.sub.4 =a maximum percent increase in compressive strength at.theta.=90.degree. and maximum porosity, due to dip angle.

n=an orientation value for the lithology;

.theta..sub.c =a critical dip angle at which compressive strength is minimum.

16. The method of claim 15 wherein said intermediate orientation signals are processed to generate said orientation adjustment signals;

said orientation adjustment signals corresponding to a maximum orientation adjustment value (at minimum porosity), and a minimum orientation adjustment value (at maximum porosity).

17. The method of claim 16 comprising generating additional signals corresponding, respectively, to:

.gamma.=a sine function of.theta., having a maximum value of 90.degree. at.theta.=.theta..sub.c,

.sigma..sub..theta. =compressive strength at.theta.;

for 0<.theta..ltoreq..theta..sub.c:

.gamma.=(.theta./.theta..sub.c).pi./

f.sub.1 =(.sigma..sub..theta.=0 -.sigma..sub..theta.=0, at minimum porosity

f.sub.2 =f.sub.1, at maximum porosity

c.sub.omax =f.sub.1 sin.sup.n (.gamma.)

c.sub.omin =f.sub.2 sin.sup.n (.gamma.)

and for.theta..sub.c <.theta..ltoreq.90.degree.:

.gamma.=.pi./2+(.theta.-.theta..sub.c)/1-.theta..sub.c 2/.pi.)

f.sub.3 =(.sigma..sub..theta.=90.degree. -.sigma..sub..theta.=0)/.sigma..sub..theta.=0, at minimum porosity

f.sub.4 =f.sub.3, at maximum porosity

c.sub.omax =f.sub.1 +f.sub.3 sin.sup.n (.gamma.)-f.sub.3

c.sub.omin =f.sub.2 +f.sub.4 sin.sup.n (.gamma.)-f.sub.4

and where:

c.sub.omax =said maximum orientation adjustment value (at minimum porosity)

c.sub.omin =said minimum orientation adjustment value (at maximum porosity)

18. The method of claim 11 comprising generating said adjustment signals also as temperature adjustment signals corresponding to functions of changes in compressive strength due to temperature.

19. The method of claim 18 comprising testing a plurality of sub-sets of a quaternary plurality of rock samples of similar lithology, the samples of each sub-set having the same porosity and confining stress but being tested at different temperatures, to determine, for each of said quaternary samples, a set of temperature variables; the generation of said temperature adjustment signals including first generating a plurality of electrical temperature variable signals occurring in pairs, the signals of each pair corresponding, respectively, to compressive strength and temperature for a respective quaternary sample.

20. The method of claim 19 wherein some of the subsets of quaternary samples have a first, relatively low, porosity, but differ, one subset from the other, in confinement stress; and others of said subsets of quaternary rock samples have a second, relatively high porosity, but differ, one subset from another, as to confinement stress.

21. The method of claim 20 comprising processing said temperature variable signals to generate signals corresponding to the temperature variables at maximum porosity and minimum porosity for said lithology.

22. The method of claim 21 comprising processing said temperature variable signals to generate intermediate temperature signals to correspond, respectively, to:

f.sub.5 =percent reduction in compressive strength at maximum test temperature and maximum test confining stress (T=T.sub.max,.sigma..sub.3 =.sigma..sub.3max), at maximum porosity (.phi.=.phi..sub.max)

f.sub.6 =percent reduction in compressive strength at maximum test temperature and standard pressure (T=T.sub.max,.sigma..sub.3 =0), at maximum porosity (.phi.=.phi..sub.max)

f.sub.7 =percent reduction in compressive strength at maximum test temperature and maximum test confinement stress (T=T.sub.max,.sigma..sub.3 =.sigma..sub.3max), at zero porosity (.phi.=0)

f.sub.8 =percent reduction in compressive strength at maximum test temperature and standard pressure (T=T.sub.max,.sigma..sub.3 =0), at zero porosity (.phi.=0)

a=a pressure-strength relationship value

b=a temperature-strength relationship value.

23. The method of claim 22 wherein said intermediate temperature signals are processed to generate said temperature adjustment signals;

said temperature adjustment signals corresponding to a maximum temperature adjustment value (at minimum porosity), and a minimum temperature adjustment value (at maximum porosity).

24. The method of claim 6 comprising so generating said adjustment signals by processing at least some of said porosity signals.

25. The method of claim 24 comprising so generating at least some of said adjustment signals as stress adjustment signals corresponding to changes in rock strength due to confinement stress.

26. The method of claim 25 comprising so generating others of said adjustment signals as orientation adjustment signals corresponding to changes in compressive strength due to dip angle of a bedding plane of the rock.

27. The method of claim 26 further comprising so generating still others of said adjustment signals as temperature adjustment signals corresponding to changes in compressive strength due to temperature.

28. The method of claim 27 comprising so generating said temperature adjustment signals as a function of at least some of said stress adjustment signals.

29. The method of claim 24 comprising so generating at least some of said adjustment signals as orientation adjustment signals corresponding to changes in compressive strength due to dip angle of a bedding plane of the rock.

30. The method of claim 24 further comprising so generating at least some of said adjustment signals as temperature adjustment signals corresponding to changes in compressive strength due to temperature.

31. The method of claim 6 comprising so generating said adjustment signals by generating and processing signals corresponding to physical properties characterizing changes in compressive strength due to confinement stress, orientation, and temperature.

32. The method of claim 31 comprising:

repeating said assaying method for at least one other lithology;

additionally determining site characteristics of the rock for a wellbore locus, at a plurality of sites along the length of said locus, and as the rock would be addressed by a drill bit, said site characteristics including porosity and physical properties similar to those so used to generate said adjustment signals, the site characteristics for each site also including values corresponding to the relative percentages of the lithologies so assayed at said site;

generating a plurality of site signals corresponding, respectively, to said site characteristics;

and processing the site signals for each site with the cumulative series of signals to generate in-situ compressive strength signals corresponding to the in-situ compressive strengths of the rock at each site.

33. The method of claim 32 comprising, for each such site, generating an electrical wellbore angle signal corresponding to the wellbore inclination angle, an electrical wellbore azimuth signal corresponding to the wellbore azimuth, an electrical bed plane angle signal corresponding to the dip angle with respect to the earth, and an electrical bed plane dip azimuth signal corresponding to the dip azimuth;

and processing said wellbore angle, wellbore azimuth, bed plane angle, and bed plane dip azimuth signals to generate an electrical relative dip angle signal corresponding to a relative dip angle of the bed plane with respect to the borehole at the respective site;

and so processing said relative dip angle signal with the cumulative series.

34. The method of claim 32 comprising generating one of the site signals as an in-situ confining stress signal corresponding to in-situ confining stress.

35. The method of claim 34 wherein said in situ confining stress signal is generated by processing a signal corresponding to effective stress due to the pressure differential between fluid in the wellbore and fluid in the surrounding formation.

36. The method of claim 34 wherein said in-situ confining stress signal is also generated by processing a signal corresponding to effective stress due to overburden.

37. The method of claim 36 wherein said in-situ confining stress signal is also generated by processing an electrical signal corresponding to effective stress due to the local geological stress field.

38. The method of claim 32 comprising so generating at least some of said site signals by processing circumferential signals corresponding to stress, other than that applied by the drill bit, acting circumferentially on the rock at the respective site.

39. The method of claim 38 comprising so generating at least some of said circumferential signals to correspond to effective stress due to the pressure differential between fluid in the wellbore and fluid in the surrounding formation.

40. The method of claim 39 comprising so generating some of said circumferential signals to correspond to effective circumferential stress due to overburden.

41. The method of claim 40 comprising so generating some of said circumferential signals to correspond to effective circumferential stress due to the local geological stress field.

42. The method of claim 38 comprising so generating at least some of said site signals by processing axial signals corresponding to axial stress, other than that applied by the drill bit, acting axially on the rock at the respective site.

43. The method of claim 42 comprising so generating at least some of said axial signals to correspond to the pressure differential between fluid in the wellbore and fluid in the surrounding formation.

44. The method of claim 43 comprising so generating some of said axial signals to correspond to effective axial stress due to overburden.

45. The method of claim 44 comprising so generating some of said axial signals to correspond to effective stress due to the local geological stress field.

46. The method of claim 42 comprising so generating at least some of said site signals by processing lateral signals corresponding to lateral stress, other than that applied by the drill bit, acting laterally on the rock at the respective site.

47. The method of claim 46 comprising so generating at least some of said lateral signals to correspond to effective lateral stress due to the pressure differential between fluid in the wellbore and fluid in the surrounding formation.

48. The method of claim 47 further comprising so generating some of said lateral signals to correspond to effective lateral stress due to overburden.

49. The method of claim 48 comprising so generating some of said lateral signals to correspond to effective lateral stress due to the local geological stress field.

50. The method of claim 34 including generating an incremental in situ compressive strength signal corresponding to the compressive strength at a point on an annulus of rock perpendicular to the wellbore at said site in one of three mutually orthogonal directions, circumferential, axial, or lateral, with respect to the wellbore axis.

51. The method of claim 50 comprising so generating said incremental in-situ compressive strength signal by processing an incremental confinement stress signal corresponding to the lesser of the stresses acting on said point in the other two of said mutually orthogonal directions.

52. The method of claim 51 wherein said generation of said incremental in situ compressive strength signal further comprises processing of signals corresponding to forces, other than applied by the drill bit, acting parallel to said one direction.

53. The method of claim 52 comprising so generating another such incremental in-situ compressive strength signal for a second of said three directions.

54. The method of claim 53 comprising so generating a third such incremental in-situ compressive strength signal for the third of said directions.

55. The method of claim 54 comprising so generating additional incremental in-situ compressive strength signals for other points on said annulus, and processing said incremental compressive strength signals to generate said in-situ compressive strength signal.

56. The method of claim 6 comprising the additionally step of determining site characteristics of the rock for a wellbore locus, at a plurality of sites along the length of said locus, and as the rock would be addressed by a drill bit, said site characteristics including porosity and physical properties similar to those so used to generate said adjustment signals;

generating a plurality of site signals corresponding, respectively, to said site characteristics;

and processing said site signals with said cumulative series of signals to generate in-situ compressive strength signals corresponding to the in-situ compressive strengths of the rock at the respective sites.

57. The method of claim 56 wherein said site characteristics are estimated, based on data from a well near said locus, and said in-situ compressive strength signals are advance in-situ compressive strength signals so generated before drilling a well along said locus.

58. The method of claim 57 comprising generating and at least partially executing a plan for drilling said well based on values corresponding to said advance in-situ compressive strength signals; and

re-evaluating said site characteristics while said drilling of said well is in progress, based on real time data for said site characteristics;

so generating a corresponding plurality of real time site signals;

so processing said real time site signals with said cumulative series of signals to generate real time in-situ compressive strength signals; and

revising said plan when the real time compressive strength signal for a given site differs sufficiently from the advance compressive strength signal for the same site.

59. The method of claim 56 comprising drilling a wellbore along said locus and so determining said site characteristics on the basis of real time data acquired while so drilling.

60. The method of claim 1 comprising the additionally step of determining site characteristics of the lithology for a wellbore locus, at a plurality of sites along the length of said locus, and as the lithology would be addressed by a drill bit, said site characteristics including porosity;

generating a plurality of site signals corresponding, respectively, to said site characteristics;

and processing said site signals with said second series of signals to generate in-situ compressive strength signals corresponding to the in-situ compressive strengths of the lithology at the respective sites.